President Barack Obama in the briefing room of the White House earlier this month.

Over the past two years, President Barack Obama has made refinancing the centerpiece of his policy response to the housing bust. Tuesday’s State of the Union address could touch on refinancing, but isn’t likely to go into specifics.

Here’s a more detailed look at what the administration has done, and what it’s likely to push for in the coming year:

Home Affordable Refinance Program

Who is eligible: Homeowners with loans that were backed by Fannie Mae and Freddie Mac before June 2009 can refinance as long as they are current on their mortgage payments. Initially, HARP was limited to borrowers who owed between 80% and 105% of their home’s current value. It was expanded in 2009 to borrowers that owed 125% of their home value, but it had disappointing results.

In late 2011, after much prodding from the Obama administration and the Federal Reserve, the companies and their regulator, the Federal Housing Finance Agency, revamped the program. The biggest of these changes eliminated the cap on loan-to-value ratios. The FHFA has implemented further changes to the so-called “HARP 2.0” initiative over the past year, and the program was on pace to enable nearly 1 million refinancing last year, more than double the volume from 2011. HARP is set to expire at the end of this year.

(The Obama administration has rolled out a similar program for borrowers with loans backed by the Federal Housing Administration. Borrowers with loans insured before June 2009 can refinance without having to pay new, higher insurance premiums.)

The verdict: Most industry analysts agree that the program has been quite successful, particularly given the underwhelming results of earlier iterations of refinance and modification programs. There have been complaints that a series of remaining frictions have allowed lenders to extract higher profits on heavily underwater loans.

The Menendez-Boxer Legislation

What it would do: After the FHFA declined to implement a handful of technical changes during HARP 2.0, the Obama administration worked with lawmakers to implement those changes through legislation. Sen. Robert Menendez (D., N.J.) and Sen. Barbara Boxer (D., Calif.) introduced legislation last year to waive certain fees that the FHFA had reduced but not eliminated entirely for HARP borrowers. The bill would also reduce certain demands placed on lenders that refinance loans they don’t currently manage and extend the HARP program for one more year. The bill does not create a new refinance program.

The verdict: The bill will likely come up for a Senate vote later this spring, but it’s less certain what will happen if it goes to the Republican-controlled House of Representatives.

‘Universal’ Refinancing Legislation

What it would do: One year ago, President Obama said that the same option that HARP had provided to borrowers with government-guaranteed loans should be extended to those who didn’t have government-backed mortgages. The government proposed that the FHA would back the newly refinanced mortgages, but with the FHA’s reserves at risk of being wiped out, that effort didn’t go anywhere.

The WSJ reported late last year that the Obama administration was looking at designing a program that would let Fannie and Freddie buy those loans. This would require Congress to change Fannie and Freddie’s charters temporarily, since the companies aren’t allowed to purchase loans that have less than 20% down payments without some form of insurance or “credit enhancement.”

The FHFA, which had indicated initial support for the general idea of the program, has been involved in discussions with Sen. Jeff Merkley (D., Ore.) about how to structure such a program, according to people familiar with the matter.

Legislation hasn’t yet been introduced, but a top Treasury adviser last month hinted that it would be coming soon.

The verdict: The odds of getting this through Congress are long. While some economists say that borrowers who are underwater but who have stayed current on their payments for this long would be good credit risks, industry officials have voiced concern about letting Fannie and Freddie expand at a time when policymakers are trying to shrink their role in the market. Such a program would reach no more than half a million borrowers, according to various industry estimates.

The Interest-Rate ‘Buy-Down’

What it would do: If Congress doesn’t approve something along the lines of the “universal” refinancing bill, the Treasury Department could move to achieve the same ends administratively.

The Treasury would use existing authority under the Home Affordable Modification Program, or HAMP, to allow borrowers to receive a reduced interest rate through a new type of loan modification for underwater borrowers who are current on their payments. The Treasury would pay the difference between the old rate and the new rate using unspent HAMP funds to mortgage investors.

The verdict: Michael Stegman, the senior Treasury official who outlined the plans last month, said that the administration would prefer the legislative route to the rate “buy-down” option, as a modification program would be probably less effective than a more-straightforward refinancing program. But the administration appears poised to use this as a fall-back option if legislation stalls out.